Magnetic Braking Formulation for Sun-Like Stars: Dependence on Dipole Field Strength and Rotation Rate

TL;DR

This paper develops a semi-analytic formula for magnetic braking in sun-like stars, based on extensive MHD simulations, accounting for magnetic field strength, rotation rate, and other stellar parameters, valid across different rotational regimes.

Contribution

It introduces a new, precise semi-analytic formulation for stellar magnetic braking that incorporates magnetic field strength and rotation rate effects, validated by comprehensive simulations.

Findings

The formula accurately fits simulation data within a few percent.

It captures the dependence of stellar wind torque on magnetic field and rotation.

Applicable to both slow and fast rotators.

Abstract

We use two-dimensional axisymmetric magnetohydrodynamic simulations to compute steady-state solutions for solar-like stellar winds from rotating stars with dipolar magnetic fields. Our parameter study includes 50 simulations covering a wide range of relative magnetic field strengths and rotation rates, extending from the slow- and approaching the fast-magnetic-rotator regimes. Using the simulations to compute the angular momentum loss, we derive a semi-analytic formulation for the external torque on the star that fits all of the simulations to a precision of a few percents. This formula provides a simple method for computing the magnetic braking of sun-like stars due to magnetized stellar winds, which properly includes the dependence on the strength of the magnetic field, mass loss rate, stellar radius, suface gravity, and spin rate and which is valid for both slow and fast rotators.